Question: Wood from a Tree . A cord of wood occupies a volume of 128 cubic feet. Forest ecologists and logging companies often want to estimate the number of cords of wood in a tree. They can do so by measuring the diameter of the tree at breast height, a point 4.5 feet above the ground. The data in the table below can be used to show the correspondence between the diameter x, in inches of a tree at breast height and the number of cords N of wood in the tree. We can fit an equation to these data points and use this model to make predictions.

Source: Warren Donnelly, Firewood for Your Fireplace

1. Enter the data into the calculator and display the scatter diagram. (No work to show for this step.)
2. Find a linear regression equation to fit the data. Write the equation you determined. Add the line to the scatter diagram and view the fit of the data to the regression line.
3. Find a exponential regression function to fit the data. Write the equation you determined.
   Graph the function on the scatter diagram to view the fit of the data to the exponential regression equation.
4. Find a quadratic regression function to fit the data. Write the equation you determined.
   Graph the function on the scatter diagram to view the fit of the data to the quadratic regression equation.
5. Which of the three regression functions fits the data best? Explain your choice.
6. Use your best fitting function to estimate the number of cords of wood from a tree that has a diameter of 40 inches at breast height. Explain how you calculated the estimate. Is it reasonable? Explain.

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